Match expressions from this list that are equivalent but written in different forms. There can be multiple matches.
I know that there is a group of 3, and a group of 2, matching expressions.
Here are the expression-I need help figuring out how to go about this.
a.) (2x^2)^3 b.) 8x^5
c.) (-4x^3)(-2x^3) d.) (6x^2)(2x^3)
e.) (12)(x)(x)(x)(x)(x)
f.) (4x)(2x^5)
Do i just simplify each expression and see what comes out equal? If so, do you have any hints on doing so?
simplifying each one to see what comes out is a great idea
I had 8x^6 three times
12x^5 twice and a single 8x^5
thank you
To match equivalent expressions, you can indeed simplify each expression to see if they are equal. Let's go through the process step by step for each expression to help you determine which expressions are equivalent:
a.) (2x^2)^3:
To simplify this expression, you need to apply the exponent rules. When raising a power to another power, you multiply the exponents. So, (2x^2)^3 becomes 2^3 * (x^2)^3 = 8x^6.
b.) 8x^5:
This expression is already in its simplified form.
c.) (-4x^3)(-2x^3):
To simplify this expression, you need to multiply the coefficients and add the exponents. (-4x^3)(-2x^3) results in 8x^6.
d.) (6x^2)(2x^3):
Similarly, when multiplying these terms, you multiply the coefficients and add the exponents. (6x^2)(2x^3) simplifies to 12x^5.
e.) (12)(x)(x)(x)(x)(x):
This expression represents the product of several x terms. To simplify, you multiply the coefficients and count the number of x terms. So (12)(x)(x)(x)(x)(x) simplifies to 12x^5.
f.) (4x)(2x^5):
Again, multiplying the terms requires multiplying the coefficients and adding the exponents. (4x)(2x^5) simplifies to 8x^6.
After simplifying each expression, you can compare the resulting expressions to find equivalent expressions. From the simplifications, expressions a and b both simplify to 8x^6, so they are equivalent. Expressions c and f also simplify to 8x^6, so they are equivalent as well.
Therefore, the two groups of matching expressions are:
Group 1: a.) (2x^2)^3 and b.) 8x^5
Group 2: c.) (-4x^3)(-2x^3) and f.) (4x)(2x^5)
Hope this helps!