Hi there!
Sure, let's simplify the expression (x^8/x^2)^2 × (x^8/x^4)^4.
First, let's simplify inside the parentheses separately.
(x^8/x^2)^2 simplifies to (x^6)^2 because when dividing with the same base, x^8 divided by x^2 equals x^(8-2) which is x^6.
Therefore, (x^8/x^2)^2 becomes x^(6*2) which is x^12.
Similarly, (x^8/x^4)^4 simplifies to (x^4)^4 because x^8 divided by x^4 equals x^(8-4) which is x^4.
Therefore, (x^8/x^4)^4 becomes x^(4*4) which is x^16.
Now let's simplify the entire expression by multiplying x^12 and x^16.
(x^12) × (x^16) = x^(12+16) = x^28.
So the simplified expression is indeed x^28.
If you're looking for an alternative form apart from x^28, there isn't one in this case. The simplification leads to x^28 as the answer.
Hi Regina
Can you simplify (x^8/x^2)^2×(x^8/x^4)^4
The answer is not x^28 can you use some kind of form that makes the answer anything but x^28??
5 answers
Simplify (x^4/x^2)^2×(x^8/x^4)^4
To simplify the expression (x^4/x^2)^2 × (x^8/x^4)^4, we can apply the rules of exponents.
First, inside the parentheses, x^4 divided by x^2 gives us x^(4 - 2) which simplifies to x^2.
Therefore, (x^4/x^2)^2 becomes (x^2)^2 which is x^(2 * 2) or x^4.
Next, inside the second set of parentheses, x^8 divided by x^4 gives us x^(8 - 4) which simplifies to x^4.
Thus, (x^8/x^4)^4 simplifies to (x^4)^4 which is x^(4 * 4) or x^16.
Now let's simplify the entire expression by multiplying x^4 and x^16.
(x^4) × (x^16) = x^(4 + 16) = x^20.
Therefore, the simplified expression is x^20.
First, inside the parentheses, x^4 divided by x^2 gives us x^(4 - 2) which simplifies to x^2.
Therefore, (x^4/x^2)^2 becomes (x^2)^2 which is x^(2 * 2) or x^4.
Next, inside the second set of parentheses, x^8 divided by x^4 gives us x^(8 - 4) which simplifies to x^4.
Thus, (x^8/x^4)^4 simplifies to (x^4)^4 which is x^(4 * 4) or x^16.
Now let's simplify the entire expression by multiplying x^4 and x^16.
(x^4) × (x^16) = x^(4 + 16) = x^20.
Therefore, the simplified expression is x^20.
SIMPLIFY (z^7)^3\cdotz^2
To simplify the expression (z^7)^3 ⋅ z^2, we can apply the rules of exponents.
First, we know that (z^7)^3 means we raise z^7 to the power of 3, which gives us (z^7)^3 = z^(7*3) or z^21.
Next, we multiply this result by z^2, so we have z^21 ⋅ z^2. Using the rule of multiplication of the same base, we add the exponents, giving us z^(21 + 2) or z^23.
Therefore, the simplified expression is z^23.
First, we know that (z^7)^3 means we raise z^7 to the power of 3, which gives us (z^7)^3 = z^(7*3) or z^21.
Next, we multiply this result by z^2, so we have z^21 ⋅ z^2. Using the rule of multiplication of the same base, we add the exponents, giving us z^(21 + 2) or z^23.
Therefore, the simplified expression is z^23.
1 answer