Simplify: (4s)3 Rewrite 5⁻³ in simplest form. Rewrite (4r)⁻² without a negative exponent. Simplify: 2(6h)⁻²

Question

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Here are the solutions to the problems:

Apply the power of a product rule, $(ab)^m = a^m b^m$ .
$(4s)^3 = 4^3 s^3$
Calculate the value of $4^3$ .
$= 64s^3$
The correct option is A.
1. Rewrite $5^{-3}$ in simplest form.
Apply the negative exponent rule, $a^{-n} = \frac{1}{a^n}$ .
$5^{-3} = \frac{1}{5^3}$
The correct option is B.
1. Rewrite $(4r)^{-2}$ without a negative exponent.
Apply the negative exponent rule, $a^{-n} = \frac{1}{a^n}$ .
$(4r)^{-2} = \frac{1}{(4r)^2}$
Apply the power of a product rule, $(ab)^m = a^m b^m$ , and calculate $4^2$ .
$= \frac{1}{4^2 r^2}$ $= \frac{1}{16r^2}$
The correct option is D.
1. Simplify: $2(6h)^{-2}$
Apply the negative exponent rule, $a^{-n} = \frac{1}{a^n}$ , to the term $(6h)^{-2}$ .
$2(6h)^{-2} = 2 \cdot \frac{1}{(6h)^2}$
Apply the power of a product rule, $(ab)^m = a^m b^m$ , and calculate $6^2$ .
$= 2 \cdot \frac{1}{6^2 h^2}$ $= 2 \cdot \frac{1}{36h^2}$
Multiply and simplify the fraction.
$= \frac{2}{36h^2}$ $= \frac{1}{18h^2}$
The correct option is A.

Answer