Make use of the calculator and determine the value of the following correct to three decimal places…

Question

Make use of the calculator and determine the value of the following correct to three decimal places: 2,705(2+6,01)⁻²,15 − 7,28 / (0,35)4

ScanSolve AI Tutor · Accepted Answer

Here are the solutions to the problems:

Question 1

1.1

Evaluate the terms in the expression.
$2.705(2 + 6.01)^{-2.15} - \frac{7.28}{(0.35)^4}$ $= 2.705(8.01)^{-2.15} - \frac{7.28}{0.01500625}$
Calculate the values using a calculator.
$= 2.705(0.00998993...) - 485.13888...$ $= 0.0270220... - 485.13888...$
Perform the subtraction and round to three decimal places.
$= -485.11186...$ $= \boxed{\mathbf{-485.112}}$
1.2
1.2.1 Convert 0.425 to a fraction.
Write the decimal as a fraction over a power of 10.
$0.425 = \frac{425}{1000}$
Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 25.
$\frac{425 \div 25}{1000 \div 25} = \frac{17}{40}$
The simplified fraction is $\boxed{\mathbf{\frac{17}{40}}}$ .

1.2.2 Convert $1.5\dot{1}\dot{3}$ to a fraction.
Let $x = 1.5131313...$ .
Multiply to isolate the repeating part.
$10x = 15.131313... \quad (1)$
Multiply by 100 (since two digits repeat) to shift the decimal past one cycle of the repeating part.
$1000x = 1513.131313... \quad (2)$
Subtract equation (1) from equation (2).
$1000x - 10x = 1513.1313... - 15.1313...$ $990x = 1498$
Solve for $x$ and simplify the fraction.
$x = \frac{1498}{990} = \frac{1498 \div 2}{990 \div 2} = \frac{749}{495}$
The simplified fraction is $\boxed{\mathbf{\frac{749}{495}}}$ .

1.2.3 Convert $0.\dot{2}\dot{6}$ to a fraction.
Let $x = 0.262626...$ .
Multiply by 100 (since two digits repeat).
$100x = 26.262626...$
Subtract $x$ from $100x$ .
$100x - x = 26.2626... - 0.2626...$ $99x = 26$
Solve for $x$ .
$x = \frac{26}{99}$
The simplified fraction is $\boxed{\mathbf{\frac{26}{99}}}$ .

Question 2

2.1 Simplify $\sqrt{\frac{32x^5y^3}{2xy}}$ .
Simplify the expression inside the square root.
$\frac{32x^5y^3}{2xy} = \frac{32}{2} \cdot \frac{x^5}{x^1} \cdot \frac{y^3}{y^1} = 16x^{5-1}y^{3-1} = 16x^4y^2$
Take the square root of the simplified expression.
$\sqrt{16x^4y^2} = \sqrt{16} \cdot \sqrt{x^4} \cdot \sqrt{y^2} = 4x^{4/2}y^{2/2} = 4x^2y$
The simplified expression is $\boxed{\mathbf{4x^2y}}$ .

2.2 Simplify $4x^3y^2 \times 2x^2y^2 \times \frac{1}{4}xy$ .
Multiply the numerical coefficients.
$4 \times 2 \times \frac{1}{4} = 8 \times \frac{1}{4} = 2$
Multiply the $x$ terms using the rule $x^a \times x^b = x^{a+b}$ .
$x^3 \times x^2 \times x^1 = x^{3+2+1} = x^6$
Multiply the $y$ terms using the rule $y^a \times y^b = y^{a+b}$ .
$y^2 \times y^2 \times y^1 = y^{2+2+1} = y^5$
Combine the simplified terms.
$2x^6y^5$
The simplified expression is $\boxed{\mathbf{2x^6y^5}}$ .

2.3 Simplify $\frac{a^2b^3(a^3b)^2}{(a^{-2}b^2)^{-4}}$ .
Simplify the numerator using exponent rules $(xy)^n = x^ny^n$ and $x^a x^b = x^{a+b}$ .
$a^2b^3(a^3b)^2 = a^2b^3(a^{3 \times 2}b^{1 \times 2}) = a^2b^3(a^6b^2) = a^{2+6}b^{3+2} = a^8b^5$
Simplify the denominator using exponent rules $(xy)^

Make use of the calculator and determine the value of the following correct to three decimal places: 2,705(2+6,01)⁻²,15 - 7,28 / (0,35)4

Step-by-step solution

Evaluate the terms in the expression.

Calculate the values using a calculator.

Perform the subtraction and round to three decimal places.

Write the decimal as a fraction over a power of 10.

Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 25.

Let $x = 1.5131313...$ .

Multiply by 100 (since two digits repeat) to shift the decimal past one cycle of the repeating part.

Subtract equation (1) from equation (2).

Solve for $x$ and simplify the fraction.

Let $x = 0.262626...$ .

Subtract $x$ from $100x$ .

Solve for $x$ .

Simplify the expression inside the square root.

Take the square root of the simplified expression.

Multiply the numerical coefficients.

Multiply the $x$ terms using the rule $x^a \times x^b = x^{a+b}$ .

Multiply the $y$ terms using the rule $y^a \times y^b = y^{a+b}$ .

Combine the simplified terms.

Simplify the numerator using exponent rules $(xy)^n = x^ny^n$ and $x^a x^b = x^{a+b}$ .

Simplify the denominator using exponent rules $(xy)^

Still stuck on this one?

More Mathematics Questions

Make use of the calculator and determine the value of the following correct to three decimal places: 2,705(2+6,01)⁻²,15 - 7,28 / (0,35)4

Step-by-step solution

Evaluate the terms in the expression.

Calculate the values using a calculator.

Perform the subtraction and round to three decimal places.

Write the decimal as a fraction over a power of 10.

Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 25.

Let x=1.5131313...x = 1.5131313...x=1.5131313....

Multiply by 100 (since two digits repeat) to shift the decimal past one cycle of the repeating part.

Subtract equation (1) from equation (2).

Solve for xxx and simplify the fraction.

Let x=0.262626...x = 0.262626...x=0.262626....

Subtract xxx from 100x100x100x.

Solve for xxx.

Simplify the expression inside the square root.

Take the square root of the simplified expression.

Multiply the numerical coefficients.

Multiply the xxx terms using the rule xa×xb=xa+bx^a \times x^b = x^{a+b}xa×xb=xa+b.

Multiply the yyy terms using the rule ya×yb=ya+by^a \times y^b = y^{a+b}ya×yb=ya+b.

Combine the simplified terms.

Simplify the numerator using exponent rules (xy)n=xnyn(xy)^n = x^ny^n(xy)n=xnyn and xaxb=xa+bx^a x^b = x^{a+b}xaxb=xa+b.

Simplify the denominator using exponent rules $(xy)^

Still stuck on this one?

More Mathematics Questions

Let $x = 1.5131313...$ .

Solve for $x$ and simplify the fraction.

Let $x = 0.262626...$ .

Subtract $x$ from $100x$ .

Solve for $x$ .

Multiply the $x$ terms using the rule $x^a \times x^b = x^{a+b}$ .

Multiply the $y$ terms using the rule $y^a \times y^b = y^{a+b}$ .

Simplify the numerator using exponent rules $(xy)^n = x^ny^n$ and $x^a x^b = x^{a+b}$ .