Question

1. identify all expressions that are equivalent to \\(\frac{15^2}{5^2}\\)

what operation do we see? _______________
what is the base of the numerator? _________
what is the base of the denominator? ________
what is the exponent in the numerator? ______
what is the exponent in the denominator? ______
do the bases match? _____________
can we subtract the exponents? ____ why? ___________________________
do the exponents match? _____________
can we rewrite the problem? ________ why? ___________________________
let’s solve:

1. (912.nso.1.1)

select all expressions that are equivalent to \\(\frac{12^2}{3^2}\\)

a. \\(4^0\\)

b. 16

c. \\(\frac{1}{4^{-2}}\\)

d. \\(4^2\\)

Explanation:

Step1: Simplify the original expression

First, rewrite the numerator: $12^2 = (4\times3)^2 = 4^2\times3^2$. Then substitute into the fraction:
$$\frac{12^2}{3^2} = \frac{4^2\times3^2}{3^2}$$
Cancel out $3^2$ from numerator and denominator:
$$\frac{4^2\times3^2}{3^2} = 4^2$$

Step2: Evaluate $4^2$

Calculate the value:
$$4^2 = 16$$

Step3: Check option C

Use negative exponent rule: $\frac{1}{a^{-n}} = a^n$. So $\frac{1}{4^{-2}} = 4^2 = 16$.

Step4: Check option A

Calculate $4^0$: any non-zero number to the 0 power is 1, so $4^0=1$, which is not equivalent.

Answer:

B. 16, C. $\frac{1}{4^{-2}}$, D. $4^2$