I made a mistake when I simplified. Find and explain my mistake. Then complete the problem correctly.
Simplify:(3m^7k^-5)^-3
Solution: 3^-3 m^4 k^-8
m^4/3^3k^8
Answer:m^4/27k^8
Are you saying that (3m^(7k)^(-5))^(-3)
is the problem given?
what is 3^3 ?
= 3*3*3
= 27
yes ray
To simplify the expression (3m^7k^-5)^-3, you need to apply the reciprocal rule for negative exponents, which states that any term with a negative exponent can be moved to the denominator by changing the sign of the exponent to positive.
Let's break down the steps:
Step 1: Simplify the base
The base of the expression is 3m^7k^-5. Since we are raising the entire base to the power of -3, we need to apply the power rule, which states that raising a power to another power can be done by multiplying the exponents. Therefore, we have:
(3^(-3))(m^(7*(-3)))(k^(-5*(-3)))
Step 2: Simplify the exponents
Now we need to simplify the exponents one by one:
3^(-3) = 1/(3^3) = 1/27
m^(7*(-3)) = m^(-21)
k^(-5*(-3)) = k^15
So, the expression becomes:
(1/27)(m^(-21))(k^15)
Step 3: Apply the reciprocal rule
To apply the reciprocal rule for negative exponents, we need to move any term with a negative exponent to the denominator. Since m^(-21) has a negative exponent, we move it to the denominator and change the sign of the exponent to positive:
(1/27)(1/m^21)(k^15)
Lastly, we can rearrange the terms:
m^21/(27k^15)
Therefore, the simplified expression is m^21/(27k^15).
It seems that there was a mistake in your original solution. Instead of m^4 in the numerator and k^8 in the denominator, the correct simplified expression should be m^21 in the numerator and k^15 in the denominator.