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Exponents - Power Law - Variable Exponent Base with Known Power to Exponent Base with Unknown Power (Level 1)

This math topic focuses on solving for unknown exponents using properties of exponents, specifically the Power Law. It involves problems where students need to find the missing exponent in expressions where a base raised to one power is set equal to the same base raised to another power. This skill is crucial for understanding how exponentiation works when variables are raised to powers, then those results are raised to additional powers. Each problem presents a base-ten number raised to a power, which is then raised again, equated to the same base raised to an unknown power. This helps solidify understanding of exponents, essential for more advanced mathematics.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

Power Law - Variable Exponent Base with Known Power to Exponent Base with Unknown Power

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Solve for the missing exponent (?)

(102)6=(103)?(10^{2})^{6} = (10^{3})^{?}