Question

which expression is equivalent to $7^{2} \cdot 7^{0}$?
$\frac{7^{0}}{7^{9}}$
$7^{0}$
$(7^{1})^{2}$
$\frac{7^{2}}{7}$
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Explanation:

Step1: Apply exponent product rule

When multiplying exponents with the same base, add the exponents: $a^m \cdot a^n = a^{m+n}$.
$7^2 \cdot 7^0 = 7^{2+0} = 7^2 = 49$

Step2: Evaluate each option

Option1: $\frac{7^0}{7^9}$

Use quotient rule: $\frac{a^m}{a^n}=a^{m-n}$.
$\frac{7^0}{7^9}=7^{0-9}=7^{-9}=\frac{1}{7^9}
eq 49$

Option2: $7^0$

Any non-zero number to the 0 power is 1.
$7^0=1
eq 49$

Option3: $(7^1)^2$

Use power rule: $(a^m)^n=a^{m \cdot n}$.
$(7^1)^2=7^{1 \times 2}=7^2=49$

Option4: $\frac{7^2}{7}$

Use quotient rule: $\frac{a^m}{a^n}=a^{m-n}$.
$\frac{7^2}{7}=7^{2-1}=7^1=7
eq 49$

Answer:

$(7^1)^2$