Apply All Exponent Rules Practice

Question

Math 8 Q1 (Pre-Algebra) / Exponent Rules

Apply the Properties of Integer Exponents to generate equivalent expressions to 37⋅3−9 with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.(1 point)

Answer 1

To simplify the expression 37⋅3−9 with positive exponents, we can use the following exponent rules:

1. Product of powers rule: am * an = am+n
2. Power of a power rule: (am)n = am*n
3. Negative exponent rule: a^-n = 1/an

Let's simplify the expression step by step:

37⋅3−9

First, let's apply the negative exponent rule to get rid of the negative exponent:

37⋅3−9 = 37 * 1/3^9

Next, let's simplify the fraction by applying the power of a power rule:

37 * 1/3^9 = 37 * 1/(3^3)^3

Now, let's apply the power of a power rule:

37 * 1/(3^3)^3 = 37 * 1/3^27

Finally, let's simplify the expression:

37 * 1/3^27 = 37/3^27

So, the simplified expression is 37/3^27.

Answer 2

37⋅3−9=___

Answer 3

To simplify 37⋅3−9, we can use the rule:

a^(-n) = 1/(a^n)

Applying this rule to the expression, we have:

37⋅3^(-9) = 37/(3^9)

Thus, the value of 37⋅3−9 is 37/(3^9).

Answer 4

1. 3^7*3^-9= 1/9
2.2^2/2^-4= 64
3.4^0*5^-2/(-2)^-3= 8/25
4.(14^3*27^-7)^0/3^4= 1/81
5.(4^3*7^-2)^-5/7^9*4^-13= 7/16