Write 6¹⁰ ÷ 6² as a single power of 6.

Simplify fully 5x³y² * 3x⁴y³

To write 6¹⁰ ÷ 6² as a single power of 6, we need to subtract the exponents.

The given expression can be written as 6^(10-2).

Simplifying, we have 6²⁶.

Therefore, 6¹⁰ ÷ 6² is equal to 6²⁶.

To simplify fully 5x³y² * 3x⁴y³, we need to combine the like terms.

Multiplying the coefficients, we have 5 * 3 = 15.

For the variables, we add the exponents.

For x, we have x³ * x⁴ = x^(3+4) = x⁷.

For y, we have y² * y³ = y^(2+3) = y⁵.

Therefore, 5x³y² * 3x⁴y³ simplifies to 15x⁷y⁵.

To simplify the expression 6¹⁰ ÷ 6² as a single power of 6, we can subtract the exponents.

Since we are dividing two powers with the same base (which is 6), we can subtract the exponents:

6¹⁰ ÷ 6² = 6^(10-2) = 6^8.

Therefore, 6¹⁰ ÷ 6² can be written as a single power of 6, which is 6^8.

Now let's simplify the expression 5x³y² * 3x⁴y³:

To simplify this expression, we can multiply the coefficients (5 * 3 = 15) and combine the variables by adding their exponents.

So, 5x³y² * 3x⁴y³ = 15x^(3+4)y^(2+3).

Simplifying further, we get:

15x^7y^5.

as always, remember that

multiplication adds exponents
division subtracts exponents

6¹⁰ ÷ 6² = 6¹ ÷ 6² = 6^(1-2) = 6^(-1)
But you might have meant
6^10 ÷ 6^2 = 6^(10-2) = 6^8

similarly,

5x³y² * 3x⁴y³ = (5*3) x^(3+4) y^(2+3) = ...