Express each power as an equivalent radical.
K. I don't know how to write this, but I'll explain.
There is a fraction. 1 over 9. And 9 has a power up to it which is 5 and a power down which is 3. I don't get how to express this power as an equivalent radical. I checked the answer at the back of the book, and it is 1 over 9 in brackets. beside it there is 1/3 in small font like a power, next to big one in 1/9. then there is 5 outside the other brackets.
To express a power as an equivalent radical, you need to understand the relationship between fractional exponents and radicals.
In this case, you have the fraction 1/9 with a power of 5 and a power of -3. Let's break it down step by step:
1. To express the numerator of the fraction (1) as a radical, we can write it as the square root of 1 since the power is 2 (equal to the square root).
2. To express the denominator of the fraction (9) as a radical, we can write it as the square root of 9 since the power is also 2. So, 9 can be written as √9.
3. The power outside the brackets (5) indicates that the entire fraction is raised to the power of 5. This means we raise both the numerator and the denominator to the power of 5.
By applying these steps, we can express the original fraction (1/9) as an equivalent radical:
√(1^5) / √(9^5)
Simplifying further, we have:
1 / 3√(9^5)
So, the answer you found in the back of the book, 1/9^(1/3), and its equivalent 1 / 3√(9^5), are both correct and represent the same value.
To express the given power as an equivalent radical, follow these steps:
Step 1: Recognize that the given expression is a fractional exponent. The base is 9, the numerator of the fraction is 1, and the denominator of the fraction is 3. This means that we have 9 raised to the power of (1/3) raised to the power of 5.
Step 2: Understand that when we have an exponent inside another exponent, we need to multiply the exponents. Therefore, we can rewrite the expression as (9^(1/3))^5.
Step 3: Recall that raising a number to the power of 1/n is equivalent to taking the nth root of that number. In this case, 9^(1/3) is the cube root of 9.
Step 4: Evaluate the cube root of 9, which is equal to 2. Therefore, we can rewrite the expression as 2^5.
Step 5: Simplify 2^5 to get the final result. 2^5 equals 32.
Therefore, the equivalent radical expression for 1/9^(5/3) is 32.