5^-1 z^7
__________
5^2 z^9
= 5^3
______
z^2
I noticed yesterday you had several problems typed this way that remained unanswered.
That is probably because none of the tutors were able to decipher it and thus left it alone.
for the above do you mean:
5^-1 z^7 /(5^2 z^9 ) = 5^3 / z^2 ??
yes, I am sorry
To simplify the expression (5^-1 z^7) / (5^2 z^9) and convert it into the form 5^3 / z^2, we can use the rules of exponents.
First, let's simplify the numerator (5^-1 z^7). Using the rule for negative exponents, we know that 5^-1 is equal to 1 / 5^1. So, the numerator becomes (1 / 5^1) z^7.
Next, let's simplify the denominator (5^2 z^9). The exponent rule states that when you divide two exponential terms with the same base, you subtract the exponents. So, 5^2 / 5^9 can be simplified to 5^(2-9) which is 5^-7. Therefore, the denominator becomes 5^-7 z^9.
Now, let's substitute the simplified numerator and denominator back into our original expression:
(1 / 5^1 z^7) / (5^-7 z^9)
Next, we can use the rule for dividing exponential terms with the same base. The rule states that when you divide two exponential terms with the same base, you subtract the exponents. So, we subtract the exponents of 5 (1 - (-7)) and subtract the exponents of z (7 - 9).
This gives us:
1 / (5^(1 - (-7)) z^(7 - 9))
Simplifying further:
1 / (5^8 z^-2)
Remember that z^-2 is equal to 1 / z^2. Substituting this:
1 / (5^8) (1 / z^2)
Finally, we can simplify the expression:
1 / (390625 z^2)
Therefore, the simplified form of (5^-1 z^7) / (5^2 z^9) is 1 / (390625 z^2), which can also be written as 5^3 / z^2.