Question

select all the expressions that are equivalent to $10^{6} \cdot 10^{8}$.
$\frac{1}{10^{48}}$
$10^{14}$
$10^{48}$
$(10^{5})^{9}$

Explanation:

Step1: Apply exponent product rule

When multiplying exponents with the same base, add the exponents: $a^m \cdot a^n = a^{m+n}$.
For $10^6 \cdot 10^8$, we calculate:
$10^{6+8} = 10^{14}$

Step2: Evaluate other options

• $\frac{1}{10^{48}} = 10^{-48}$, which is not equal to $10^{14}$.
• $10^{48}$ is not equal to $10^{14}$.
• $(10^5)^9 = 10^{5 \times 9} = 10^{45}$, which is not equal to $10^{14}$.

Answer:

$10^{14}$