Q. Simplify. Express your answer using positive exponents.q9q9⋅q−9
Identify Operation: Identify the operation needed for the exponents.When we multiply powers with the same base, we add the exponents. When we divide powers with the same base, we subtract the exponents.
Simplify Numerator: Simplify the numerator q9⋅q−9. We add the exponents because the bases are the same and we are multiplying. q9⋅q−9=q9+(−9)=q0 Any number to the power of 0 is 1, so q0=1.
Divide by q9: Divide the result from Step 2 by q9. Since q0=1, we have q91. When we divide by a power, we subtract the exponents, but since the numerator is 1 (which is q0), we have q0−9=q−9. However, we need to express the answer with positive exponents.
Express with Positive Exponent: Express q−9 with a positive exponent.A negative exponent means that the base is on the wrong side of the fraction line. To make the exponent positive, we can rewrite q−9 as 1/q9.
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