Simplify the following algebraic expressions: 1) 9p8q5r2/3p8q5r2 2) 2(m3)0 - (2m3)0 3) (−4)2 x (2)2 + (−3)0.

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Here are the solutions to the problems.

1) Simplify $\frac{9p^8q^5r^2}{3p^8q^5r^2}$ .

Separate the coefficients and variables.
$\frac{9p^8q^5r^2}{3p^8q^5r^2} = \frac{9}{3} \times \frac{p^8}{p^8} \times \frac{q^5}{q^5} \times \frac{r^2}{r^2}$
Simplify each part.
$\frac{9}{3} = 3$ $\frac{p^8}{p^8} = p^{8-8} = p^0 = 1$ $\frac{q^5}{q^5} = q^{5-5} = q^0 = 1$ $\frac{r^2}{r^2} = r^{2-2} = r^0 = 1$
Multiply the simplified parts.
$3 \times 1 \times 1 \times 1 = 3$
The simplified expression is $\boxed{3}$ .

2) Simplify $2(m^3)^0 - (2m^3)^0$ .
Apply the exponent rule $(a^b)^0 = 1$ and $a^0 = 1$ .
For the first term, $(m^3)^0 = 1$ . So, $2(m^3)^0 = 2 \times 1 = 2$ .
For the second term, $(2m^3)^0 = 1$ because the entire term inside the parentheses is raised to the power of 0.
Substitute the simplified terms back into the expression.
$2 - 1$
Perform the subtraction.
$2 - 1 = 1$
The simplified expression is $\boxed{1}$ .

3) Simplify $(-4)^2 \times (2)^2 + (-3)^0$ .
Evaluate each term.
$(-4)^2 = (-4) \times (-4) = 16$ $(2)^2 = 2 \times 2 = 4$ $(-3)^0 = 1 \quad (\text{Any non-zero number raised to the power of 0 is 1})$
Substitute the values back into the expression.
$16 \times 4 + 1$
Perform the multiplication.
$16 \times 4 = 64$
Perform the addition.
$64 + 1 = 65$
The simplified expression is $\boxed{65}$ .

4) Simplify $(31260xy)^0 \times (5x^2)$ .
Apply the exponent rule $a^0 = 1$ .
For the first term, $(31260xy)^0 = 1$ because the entire term inside the parentheses is raised to the power of 0.
Substitute the simplified term back into the expression.
$1 \times (5x^2)$
Perform the multiplication.
$1 \times 5x^2 = 5x^2$
The simplified expression is $\boxed{5x^2}$ .

5) Simplify $\frac{50x^8y^3z^2}{25x^8y^3z^2}$ .
Separate the coefficients and variables.
$\frac{50x^8y^3z^2}{25x^8y^3z^2} = \frac{50}{25} \times \frac{x^8}{x^8} \times \frac{y^3}{y^3} \times \frac{z^2}{z^2}$
Simplify each part.
$\frac{50}{25} = 2$ $\frac{x^8}{x^8} = x^{8-8} = x^0 = 1$ $\frac{y^3}{y^3} = y^{3-3} = y^0 = 1$ $\frac{z^2}{z^2} = z^{2-2} = z^0 = 1$
Multiply the simplified parts.
$2 \times 1 \times 1 \times 1 = 2$
The simplified expression is $\boxed{2}$ .

Simplify the following algebraic expressions: 1) (9p8q5r2)/(3p8q5r2) 2) 2(m3)0 - (2m3)0 3) (-4)2 x (2)2 + (-3)0.

Step-by-step solution

Separate the coefficients and variables.

Simplify each part.

Multiply the simplified parts.

Apply the exponent rule $(a^b)^0 = 1$ and $a^0 = 1$ .

Substitute the simplified terms back into the expression.

Perform the subtraction.

Evaluate each term.

Substitute the values back into the expression.

Perform the multiplication.

Perform the addition.

Apply the exponent rule $a^0 = 1$ .

Substitute the simplified term back into the expression.

Perform the multiplication.

Separate the coefficients and variables.

Simplify each part.

Multiply the simplified parts.

Still stuck on this one?

More Mathematics Questions

Simplify the following algebraic expressions: 1) (9p8q5r2)/(3p8q5r2) 2) 2(m3)0 - (2m3)0 3) (-4)2 x (2)2 + (-3)0.

Step-by-step solution

Separate the coefficients and variables.

Simplify each part.

Multiply the simplified parts.

Apply the exponent rule (ab)0=1(a^b)^0 = 1(ab)0=1 and a0=1a^0 = 1a0=1.

Substitute the simplified terms back into the expression.

Perform the subtraction.

Evaluate each term.

Substitute the values back into the expression.

Perform the multiplication.

Perform the addition.

Apply the exponent rule a0=1a^0 = 1a0=1.

Substitute the simplified term back into the expression.

Perform the multiplication.

Separate the coefficients and variables.

Simplify each part.

Multiply the simplified parts.

Still stuck on this one?

More Mathematics Questions

Apply the exponent rule $(a^b)^0 = 1$ and $a^0 = 1$ .

Apply the exponent rule $a^0 = 1$ .