Q1. The answer is 7 to the 5 over 4 power
Let's write the fourth root of 7 to the fifth power as a radical. 7 to the fifth power is 7⁵. The fourth root of 7 to the fifth power is
.
Now, to rewrite it as a rational exponent, we will use the following:
Our radical is
which means that n = 4, m = 5.
So, the rational exponent it will be:
which is the same as 7 to the 5 over 4 power
Q2. The answer is the eighth root of 2 to the fifth power.
Let's present 2 to the 7 over 8 power, all over 2 to the 1 over 4 power as a rational exponent.
2 to the 7 over 8 power is
2 to the 1 over 4 power is
2 to the 7 over 8 power, all over 2 to the 1 over 4 power is
Using the rule:
we have:
Since:
, then n = 8, m = 5
Therefore
Q3. The answer is 9 inches squared.
The area of the rectangle (A) is
A = l · w (l - length, w - width).
It is given:
l = the cube root of 81 inches =
w = 3 to the 2 over 3 =
A =
Since:
then:
A =
Q4. The answer is By simplifying 25 to 5² to make both powers base five and subtracting the exponents
5 to the fourth power, over 25 = 52 is
Now, let's simplify 25 to 5²:
Since
, we will subtract the exponents:
⇒
Q5. The answer is the ninth root of 3
3 to the 2 over 3 power is
3 to the 2 over 3 power, to the 1 over 6 power is
Since
then:
Since:
, then: n = 9, m = 1