Question

compare the value of each expression to 64. write the expression in the correct box.
$2^3 \cdot 2^2$ $\frac{4^7}{4^3}$ $(8^2)^2$ $64^0$ $(2 \cdot 4)^3$
less than 64 greater than 64

Explanation:

Step1: Simplify $2^3 \cdot 2^2$

Use exponent rule $a^m \cdot a^n = a^{m+n}$:
$2^{3+2}=2^5=32$

Step2: Simplify $\frac{4^7}{4^3}$

Use exponent rule $\frac{a^m}{a^n}=a^{m-n}$:
$4^{7-3}=4^4=256$

Step3: Simplify $(8^2)^2$

Use exponent rule $(a^m)^n=a^{m \cdot n}$:
$8^{2 \cdot 2}=8^4=4096$

Step4: Simplify $64^0$

Use exponent rule $a^0=1$ ($a
eq0$):
$64^0=1$

Step5: Simplify $(2 \cdot 4)^3$

First calculate inside parentheses:
$(8)^3=512$

Step6: Compare to 64

Classify each result against 64.

Answer:

Less Than 64:

$2^3 \cdot 2^2$, $64^0$

Greater Than 64:

$\frac{4^7}{4^3}$, $(8^2)^2$, $(2 \cdot 4)^3$