Question Video: Evaluating an Expression with a Positive Decimal Base and a Positive Decimal Exponent | Nagwa Question Video: Evaluating an Expression with a Positive Decimal Base and a Positive Decimal Exponent | Nagwa

# Question Video: Evaluating an Expression with a Positive Decimal Base and a Positive Decimal Exponent Mathematics

Evaluate (0.0625)^(0.25).

01:37

### Video Transcript

Evaluate 0.0625 to the power 0.25.

Our approach to evaluating this will involve taking both of our decimals, the base and the exponent, and writing those as fractions. So 0.0625 is equivalent to 625 over 10000, and our exponent of 0.25 is equivalent to one-quarter. We can then apply some exponent rules.

The first rule weโre going to use is that if we have a fraction ๐ฅ over ๐ฆ to the power of ๐, this is equivalent to ๐ฅ to the power of ๐ over ๐ฆ to the power of ๐. So our fraction is equivalent to 625 to the power of one-quarter over 10000 to the power of one-quarter.

Now letโs think about what it means to be to the power of one-quarter. We can use our second rule to help us here, which says that if we have a value ๐ฅ to the power of one over ๐, itโs equivalent to the ๐th root of ๐ฅ. So our fractional exponent of one-quarter is equivalent to the fourth root.

On the numerator then, we have the fourth root of 625. And on the denominator, itโs the fourth root of 10000. Evaluating the fourth root of 625 gives us five, since if we write five down four times and multiply, weโll get 625. And then the fourth root of 10000 is 10 since again if we write down 10 four times and multiply, we get 10000. We can then simplify our fraction five-tenths, giving us a final answer of a half.

## Join Nagwa Classes

Attend live sessions on Nagwa Classes to boost your learning with guidance and advice from an expert teacher!

• Interactive Sessions
• Chat & Messaging
• Realistic Exam Questions