next, write the expression as a single power of 10.$(10^{2})^{3} = 10^{2}cdot10^{2}cdot10^{2}$=…
next, write the expression as a single power of 10.$(10^{2})^{3} = 10^{2}cdot10^{2}cdot10^{2}$= ?options:$10^{3}$$10^{4}$$10^{5}$$10^{6}$
Answer
Explanation:
Step1: Add exponents when multiplying
When multiplying powers with the same base, add the exponents: $10^2 \cdot 10^2 \cdot 10^2 = 10^{2+2+2}$
Step2: Calculate the sum of exponents
$2+2+2=6$, so $10^{2+2+2}=10^6$ Alternatively, use power of a power rule: $(10^2)^3=10^{2 \times 3}=10^6$
Answer:
$10^6$