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HSPT Math : HSPT Mathematics

Study concepts, example questions & explanations for HSPT Math

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All HSPT Math Resources

6 Diagnostic Tests 130 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1261 : Hspt Mathematics

$25f*20f^{3}=$

Possible Answers:

$500f^{4}$

$45f^{3}$

$500f^{6}$

$45f^{4}$

$500f^{3}$

Correct answer:

$500f^{4}$

Explanation:

Multiply the constants and add an exponent to the variable totaling the number of variables in the equation:

$25f*20f^{3}=500f^{4}$

Answer: $500f^{4}$

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Example Question #1262 : Hspt Mathematics

Simplify:

$(4v^{3})(xy^{2}v)(2x^{3}v)$

Possible Answers:

$6x^{2}y^{2}v^{3}$

$x^{6}y^{2}v^{14}$

$8x^{2}y^{2}v^{3}$

$9x^{2}y^{2}v^{3}$

$8x^{4}y^{2}v^{5}$

Correct answer:

$8x^{4}y^{2}v^{5}$

Explanation:

Begin by moving all of the related variables (and constants) next to each other. You can group these in parentheses to make it clear. This is allowed because of the associative rule for multiplication.

$(4 * 2) (v^{3}*v*v)(x*x^{3})(y^{2})$

When multiplying variables of the same type, you add their exponents together. This gets you:

$(8)(v^{3+1+1})(x^{1+3})(y^2)$

$(8) (v^{5})(x^{4})(y^{2})$

This is the same as:

$8x^{4}y^{2}v^{5}$

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Example Question #57 : Algebra

Simplify:

$e * t * f^{4} * t^{2} * 10 * f$

Possible Answers:

$ef^{21}t^{3}$

$e^{10}f^{5}t^{3}$

$ef^{14}t^{3}$

$10ef^{4}t^{2}$

$10ef^{5}t^{3}$

Correct answer:

$10ef^{5}t^{3}$

Explanation:

$(10)(e)(f^{4} *f)(t * t^{2})$

When multiplying variables of the same type, you add their exponents together. This gets you:

$(10)(e)(f^{4+1})(t^{1+2})$

$(10)(e)(f^{5})(t^{3})$

This is the same as:

$10ef^{5}t^{3}$

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Example Question #668 : Concepts

Simplify:

4e*f*e*e*f*f*f*e*3*e*e*e*f*f

Possible Answers:

18ef

$7e^{7}f^{6}$

$12e^{7}f^{6}$

20ef

$4e^{9}f^{6}$

Correct answer:

$12e^{7}f^{6}$

Explanation:

(4 *3)(e*e*e *e*e*e*e) (f*f*f*f**f*f)

When multiplying variables of the same type, you add their exponents together. (All of these variables have exponents of 1.) This gets you:

$(12)(e^{1+1+1+1+1+1+1})(f^{1+1+1+1+1+1})$

$(12)(e^{7}) (f^{6})$

This is the same as:

$12e^{7}f^{6}$

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Example Question #1263 : Hspt Mathematics

Simplify:

$2(f^{6})(u^{7})(e^{2}f^{2})(eu)$

Possible Answers:

$e^{3}f^{14}u^{8}$

$2e^{2}f^{24}u^{7}$

$2e^{3}f^{8}u^{6}$

$2e^{3}f^{8}u^{8}$

$2e^{2}f^{12}u^{7}$

Correct answer:

$2e^{3}f^{8}u^{8}$

Explanation:

$(2)(e * e^{2})(f^{6}*f^{2})(u*u^{7})$

When multiplying variables of the same type, you add their exponents together. This gets you:

$(2)(e^{1+2})(f^{6+2})(u^{1+7})$

$(2)(e^{3})(f^{8})(u^{8})$

This is the same as:

$2e^{3}f^{8}u^{8}$

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Example Question #672 : Concepts

Simplify:

$(4g)(2r^{2})(r^{3})(g^{2})$

Possible Answers:

$4g^{5}r^{5}$

$8g^{3}r^{5}$

$8g^{2}r^{6}$

$8g^{2}r^{5}$

$6g^{3}r^{5}$

Correct answer:

$8g^{3}r^{5}$

Explanation:

$(2*4)(g*g^{2})(r^{2}*r^{3})$

When multiplying variables of the same type, you add their exponents together. This gets you:

$(8)(g^{1+2})(r^{2+3})$

$(8)(g^{3})(r^{5})$

This is the same as:

$8g^{3}r^{5}$

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Example Question #31 : How To Multiply Variables

Simplify:

$(2)(15y^{2})(x^{3})(10)$

Possible Answers:

$300x^{3}y^{2}$

$27 x^{4}y^{2}$

$27x^{3}y^{2}$

$30x^{31}y^{2}$

$20x^{4}y^{30}$

Correct answer:

$300x^{3}y^{2}$

Explanation:

$(2 * 15 * 10)(x^{3})(y^{2})$

There are no variables to combine. We only need to combine the numerical coefficient. This gets you:

$(300)(x^{3})(y^{2})$

This is the same as:

$300x^{3}y^{2}$

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Example Question #671 : Concepts

Simplify:

$x * y * (x^{3}) * (xy)$

Possible Answers:

$6x^{3}y$

$3x^{5}y^{2}$

10xy

$x^{3}y$

$x^{5}y^{2}$

Correct answer:

$x^{5}y^{2}$

Explanation:

$(x * x* x^{3})(y * y)$

When multiplying variables of the same type, you add their exponents together. This gets you:

$(x^{1+1+3})(y^{1+1})$

$(x^{5})(y^{2})$

This is the same as:

$x^{5}y^{2}$

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Example Question #1267 : Hspt Mathematics

Simplify:

$x * a^{3} * y^{4} * x^{2} * x*a^{2}$

Possible Answers:

$a^{6}xy^{2}$

$a^{6}x^{2}y^{4}$

80axy

$a^{5}x^{3}y^{4}$

$a^{5}x^{4} y^{4}$

Correct answer:

$a^{5}x^{4} y^{4}$

Explanation:

$(a^{3} * a^{2})(x * x^{2} * x)(y^{4})$

When multiplying variables of the same type, you add their exponents together. This gets you:

$(a^{3+2})(x^{1+2+1})(y^4)$

$(a^{5})(x^{4})(y^{4})$

This is the same as:

$a^{5}x^{4} y^{4}$

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Example Question #32 : How To Multiply Variables

Simplify:

$xy(x^{2} + 2aby)$

Possible Answers:

$3abx^{3}y^{2}$

$x^{2}y + 2abxy$

$3abx^{3}y$

$2x^{2}y + 4abxy$

$x^{3}y + 2abxy^{2}$

Correct answer:

$x^{3}y + 2abxy^{2}$

Explanation:

$xy(x^{2} + 2aby)$

Distribute the outside term into the parentheses. Multiply each term in parentheses by :

$(xy)(x^{2}) + (xy)(2aby)$

Now, for each member, move the similar variables into separate groups. You can do this because of the associative rule for multiplication:

$(x*x^{2})(y) + (2)(a)(b)(x)(y*y)$

When multiplying variables of the same type, you add their exponents together. This gets you:

$(x^{1+2})(y)+(2)(a)(b)(x)(y^{1+1})$

$(x^{3})(y) + (2)(a)(b)(x)(y^2)$

This is the same as:

$x^{3}y + 2abxy^{2}$

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HSPT Math : HSPT Mathematics

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #1261 : Hspt Mathematics

Example Question #1262 : Hspt Mathematics

Example Question #57 : Algebra

Example Question #668 : Concepts

Example Question #1263 : Hspt Mathematics

Example Question #672 : Concepts

Example Question #31 : How To Multiply Variables

Example Question #671 : Concepts

Example Question #1267 : Hspt Mathematics

Example Question #32 : How To Multiply Variables

All HSPT Math Resources

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