I don't understand how I am supposed to solve if i have something like (-7) to the power of -2... or 3/4 to the power of -1
-7^ (-2), put it divided by 1.
-1/(7^2) when you place the exponent to the denominator, change the sign, same goes if you have a negative exponent on the denominator, bring it to the numerator and change the sign.
-1/49
(3/4)^(-1). Just switch the fraction to
4/3 , because its the whole fraction raised to -1.
if ( 3^(-1) ) / 4 ==> 1/(3*4)=1/12
To solve expressions with negative exponents, follow these steps:
1. For any negative exponent, rewrite the expression by moving the term with the negative exponent to the opposite side of the fraction.
Let's apply these steps to your examples:
Example 1: (-7)^-2
First, we have to move the term with the negative exponent, (-7), to the opposite side of the fraction:
1/(-7)^2
Example 2: (3/4)^-1
Again, we move the term with the negative exponent, (3/4), to the opposite side of the fraction:
1/(3/4)^1
Now, let's simplify each of the expressions using the rules of exponents:
Example 1: (-7)^-2
To evaluate (-7)^2, we simply raise the number 7 to the power of 2:
(-7)^2 = 49
So, the simplified expression is 1/49.
Example 2: (3/4)^-1
To evaluate (3/4)^1, we raise the fraction 3/4 to the power of 1. Since any number raised to the power of 1 remains the same, we can rewrite it as:
(3/4)
Now, we need to find the reciprocal of (3/4) because of the negative exponent. To find the reciprocal, we swap the numerator and the denominator, resulting in:
4/3
So, the simplified expression is 4/3.
In summary, to solve expressions with negative exponents, move the term with the negative exponent to the opposite side of the fraction and apply the corresponding exponent rule.