Answer:
m = 3.
Step-by-step explanation:
[tex] {9}^{m} \div {3}^{ - 2} = {9}^{4} \\ 3 = {9}^{ \frac{1}{2} } \\ {9}^{m} \div {9}^{ \frac{1}{2} \times ( - 2)} = {9}^{4} \\ {9}^{m} \div {9}^{ - 1} = {9}^{4} \\ recall \: {x}^{a} \div {x}^{b} = {x}^{a - b} \\ {9}^{m - ( - 1)} = {9}^{4} \\ {9}^{m + 1} = {9}^{4} \\ since \: the \: bases \: are \: the \: same... \\ m + 1 = 4 \\ m = 4 - 1 \\ m = 3 \\ \\ [/tex]
I Hope You Understand .
Step-by-step explanation:
To find the value of m in the equation [tex] \: 9^{m} ÷ 3^{-2} = 9^{4} \: [/tex] we can start by simplifying both sides of the equation.
First, let's simplify [tex] \: 9^{4} \: [\tex] on the right side of the equation :
Now our equation becomes:
[tex] \tt 9^{m} ÷ 3^{-2} \: = \: 6561 [/tex]
Next, we can simplify 3^(-2) on the left side of the equation: 3^(-2) = 1/3^2 = 1/9.
Substituting this back into the equation:
[tex] \tt \: 9^{m} \: /divide \: \frac{1}{9} \: = \: 6561 \: [/tex]
We can simplify the division by multiplying the numerator by the reciprocal of the denominator:
[tex] \tt \: 9^{m} \times 9 \: = \: 6561 \: [/tex]
Applying the power rule of exponents, we multiply the exponents when raising a power to another power:
[tex] \: 9^{m\: + \: 1} \: = \: 6561 \: [/tex]
Since 9 is equal to 3^2, we can write the equation as:
[tex] \tt \: 3^{2}^{m+1} = 6561 \: [/tex]
Applying the power rule of exponents again, we multiply the exponents:
3^(2(m+1)) = 6561
Since 6561 is also equal to 3^8, we can write the equation as:
3^(2(m+1)) = 3^8
Now we can equate the exponents:
2(m+1) = 8
Simplifying the equation:
2m + 2 = 8
Subtracting 2 from both sides:
2m = 6
Dividing by 2:
m = 3
Therefore, the value of m in the equation 9^m ÷ 3^(-2) = 9^4 is 3.
