1. Use the Product Rule of Exponents to simplify 6^10 x 6^5 (put answer in exponent form)
To simplify the expression 6^10 x 6^5 using the Product Rule of Exponents, you add the exponents of the same base.
We have 6^10 x 6^5. In this case, the base is 6. So we add the exponents:
10 + 5 = 15.
Therefore, 6^10 x 6^5 can be simplified to 6^15.
Find the numerical equivalent of 8^9 x 8^-6
To find the numerical equivalent of 8^9 x 8^-6, we simplify each term separately and then multiply them together.
First, let's simplify 8^9:
8^9 = 8 x 8 x 8 x 8 x 8 x 8 x 8 x 8 x 8
This is equivalent to multiplying 8 by itself 9 times.
Next, let's simplify 8^-6:
8^-6 = 1 / (8^6)
This is equivalent to taking the reciprocal of 8^6.
Now, let's calculate 8^6:
8^6 = 8 x 8 x 8 x 8 x 8 x 8
This is equivalent to multiplying 8 by itself 6 times.
So, 8^6 = 8 x 8 x 8 x 8 x 8 x 8 = 262,144.
Taking the reciprocal of 262,144 gives us:
8^-6 = 1 / 262,144 = 0.0000038147 (rounded to 10 decimal places).
Now, let's multiply 8^9 by 8^-6:
8^9 x 8^-6 = (8 x 8 x 8 x 8 x 8 x 8 x 8 x 8 x 8) x (1 / 262,144)
= 134,217,728 x 0.0000038147
= 512 (rounded to the nearest whole number).
Therefore, the numerical equivalent of 8^9 x 8^-6 is 512.
Find the value of x to make this exponential equation true… 5^x ÷ 5^5 = 5^12
To make the equation 5^x ÷ 5^5 = 5^12 true, we can use the Quotient Rule of Exponents.
According to the Quotient Rule, when dividing two terms with the same base, we subtract the exponents.
So, from the equation 5^x ÷ 5^5 = 5^12, we have:
5^(x - 5) = 5^12.
For this equation to be true, the exponents on both sides must be equal. Therefore, we can set:
x - 5 = 12.
To isolate x, we can add 5 to both sides:
x - 5 + 5 = 12 + 5,
x = 17.
So, the value of x that makes the exponential equation 5^x ÷ 5^5 = 5^12 true is x = 17.
Use the Power Rule of Exponents to simplify (9^3)^6 . Answer in exponent form.
To simplify (9^3)^6 using the Power Rule of Exponents, we multiply the exponents:
(9^3)^6 = 9^(3*6).
This simplifies to:
9^(18).
Therefore, (9^3)^6 can be simplified to 9^18 in exponent form.