Raise both powers to the inverse of the exponent on the left-hand side.
D
d
Raise both powers to the inverse of the exponent on the left-hand side.
E
e
Raise both powers to the inverse of the exponent on the left-hand side.
A
a
1/8
B
b
1/x
C
c
m≈ ± 1.59
D
d
n ≈ ± 2.59
E
e
See solution.
Practice makes perfect
a
Let's name the number we need to multiply 8 by to get 1 as n. We want to know what we should multiply n by to get 1. We can write the following equation.
8n=1
By solving this equation for n, we can determine what this number is.
Examining the equation, we see that m is raised to the power of 8. To solve for m we have to eliminate the exponent. We can do that by taking the 8^(th) root of both sides. Notice that because the exponent is even we get two solutions.
sqrt(m^8)=± sqrt(40)
⇕
m=± sqrt(40)
However many, if not all, calculators do not have the 8^(th) root as a button. Instead, we can raise both sides to the inverse of 8, which is the equivalent to taking the 8^(th) root.
(m^8)^(18)=± (40)^(18)
⇕
m=± (40)^(18)
Using a calculator, we can determine the right-hand side.
As we can see, m≈ ± 1.5858.... We can check it by raising the two solutions to the power of 8 on our calculator.
d
From Part C, we know that to eliminate an exponent we have to raise the power to the inverse of the exponent. Additionally, if the exponent is even, we get a positive and a negative solution.
(n^6)^(16)=± (300)^(16)
⇕
m=± (300)^(16)
Again, we will use the calculator to solve this.
We get the solutions n ≈ ± 2.59.
e
As we talked about in previous parts, we have to raise a power to the inverse of its exponent to solve for x. Additionally, if a is even, we get a positive and a negative solution.
a is even:& x^a=b x=± b^(1a)
a is odd:& x^a=b x= b^(1a)
