Simplify the following expressions: 3) 9x x 6x x a2 x b3, 4) (9x6y)ⁿ, 5) (3/10)5

Question

ScanSolve AI Tutor · Accepted Answer

Here are the solutions to the problems:

: Simplify $9x \times 6x \times a^2 \times b^3$

Multiply the numerical coefficients.
$9 \times 6 = 54$
Multiply the terms with the same variable.
$x \times x = x^{1+1} = x^2$
Combine all terms.
$54 \times x^2 \times a^2 \times b^3$ $54a^2b^3x^2$
The simplified expression is:
$\boxed{54a^2b^3x^2}$
: Simplify $(9x6y)^n$
Multiply the numerical coefficients inside the parenthesis.
$9 \times 6 = 54$
Rewrite the expression with the simplified numerical coefficient.
$(54xy)^n$
Apply the exponent $n$ to each factor inside the parenthesis.
$54^n x^n y^n$
The simplified expression is:
$\boxed{54^n x^n y^n}$
: Simplify $(\frac{3}{10})^5$
Apply the exponent to both the numerator and the denominator.
$\frac{3^5}{10^5}$
Calculate the value of the numerator.
$3^5 = 3 \times 3 \times 3 \times 3 \times 3 = 243$
Calculate the value of the denominator.
$10^5 = 10 \times 10 \times 10 \times 10 \times 10 = 100,000$
Write the simplified fraction.
$\frac{243}{100,000}$
The simplified expression is:
$\boxed{\frac{243}{100,000}}$

Simplify the following expressions: 3) 9x x 6x x a2 x b3, 4) (9x6y)ⁿ, 5) ((3)/(10))5