Simplify $\left(h^5\right)^{10}$.
Answer (1)
Apply the power of a power rule: ( a m ) n = a m × n .
Multiply the exponents: 5 × 10 = 50 .
Simplify the expression: ( h 5 ) 10 = h 5 × 10 = h 50 .
The simplified expression is h 50 .
Explanation
Understanding the Problem We are asked to simplify the expression ( h 5 ) 10 . This involves applying the power of a power rule in exponents.
Applying the Power of a Power Rule The power of a power rule states that when you raise a power to another power, you multiply the exponents. Mathematically, this is expressed as ( a m ) n = a m × n , where a is the base and m and n are the exponents.
Calculating the Exponent In our case, the base is h , and the exponents are 5 and 10 . Applying the power of a power rule, we get:
( h 5 ) 10 = h 5 × 10
Now, we multiply the exponents: 5 × 10 = 50 .
Final Result Therefore, the simplified expression is h 50 .
Examples
Understanding exponent rules is crucial in many scientific and engineering applications. For instance, when calculating compound interest, the formula often involves raising a rate to the power of time. Similarly, in physics, understanding exponential growth or decay (like in radioactive decay) requires a solid grasp of exponent rules. Simplifying expressions like the one in this problem is a fundamental skill that supports more complex calculations in these fields.
