Question

A)2^-4×2^6= B) 3^-2÷3^-4= c) 6^-4×2^-1/12^-3=

Answer 1

. А. 4.
. В. 9.
. С. 0,6.

Answer 2

To simplify the expressions, we can use the rules of exponents:

A) 2^-4 × 2^6

When you multiply two numbers with the same base, you add the exponents:

2^-4 × 2^6 = 2^(6-4) = 2^2 = 4

B) 3^-2 ÷ 3^-4

When you divide two numbers with the same base, you subtract the exponents:

3^-2 ÷ 3^-4 = 3^(-2-(-4)) = 3^(-2+4) = 3^2 = 9

C) 6^-4 × 2^-1 ÷ 12^-3

To simplify this expression, let's rewrite 12 as 6 × 2:

6^-4 × 2^-1 ÷ (6 × 2)^-3

Now, using the rule (a × b)^n = a^n × b^n:

6^-4 × 2^-1 ÷ 6^-3 × 2^-3

When you divide two numbers with the same base, you subtract the exponents:

2^(-1 - (-3)) = 2^(2) = 4

So the simplified expression is 4.