Question

1)6^5 * 6^-8 / 6^-2 = 2) (2√3)² * 5

Answer 1

1) 6^(5+(-8)-(-2))= 6^(5+2-8)=6^(-1)=1/6

2) 4*3*5= 60

Answer 2

Let's solve each expression step by step:

1. $6^5 \times 6^{-8} \div 6^{-2}$

To simplify this expression, we can use the properties of exponents. When you divide two numbers with the same base and different exponents, you can subtract the exponents:

$a^m \div a^n = a^{m - n}$

So, in our case:

$6^5 \times 6^{-8} \div 6^{-2} = 6^{5 - (-8 + 2)}$

Now, simplify the exponents inside the parentheses:

$6^{5 - (-8 + 2)} = 6^{5 + 8 - 2}$

$6^{5 + 8 - 2} = 6^{11}$

Now the expression is simplified to $6^{11}$. You can calculate it as:

$6^{11} = 362,797,056$.

Therefore, $6^5 \times 6^{-8} \div 6^{-2} = 362,797,056$.

2. $(2\sqrt{3})^2 \times 5$

First, evaluate the square of $2\sqrt{3}$:

$(2\sqrt{3})^2 = 2^2 \times (\sqrt{3})^2 = 4 \times 3 = 12$.

Now, multiply this result by 5:

$(2\sqrt{3})^2 \times 5 = 12 \times 5 = 60$.

Therefore, $(2\sqrt{3})^2 \times 5 = 60$.